Mesoprimary decomposition of binomial submodules

JOURNAL OF ALGEBRA

卷:480

Article

O'Neill, Christopher¹ 

[1] Texas A&M Univ, Math Dept, College Stn, TX 77840 USA

关键词: Binomial ideals;    Monoid congruences;    Combinatorial commutative algebra;   

DOI  :  10.1016/j.jalgebra.2017.02.010

来源: Elsevier

【 摘 要 】

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing mesoprimary decompositions determined by their underlying monoid congruences. Mesoprimary decompositions are highly combinatorial in nature, and are designed to parallel standard primary decomposition over Noetherean rings. In this paper, we generalize mesoprimary decomposition from binomial ideals to binomial submodules of certain graded modules over a monoid algebra, analogous to the way primary decomposition of ideals over a Noetherean ring R generalives to R-modules. The result is a combinatorial method of constructing primary decompositions that, when restricting to the special case of binomial ideals, coincides with the method introduced by Kahle and Miller. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free